Rotary pumps of the general type described above are not new per se. For example, there is shown in West German Offenlegungsschift No. 3,014,520, a rotary pump having an inlet slit as viewed in the direction of rotation which extends radially outwardly in relation to the rotational axis of the rotor so that the end on the slit pointing away against the direction of rotation is oriented at an acute angle to the cylindrical side surface of the rotor adjacent the lateral surface. In this pump, the radially outwardly pivoting vanes pass over the inlet slit at a relatively late point, that is to say at a relatively large vane distance from the central plane passing through the rotational axis of the rotor and the axis of the housing bore. Consequently, as a result of a suction effect, restoring moments in the working chamber forming the vanes but not yet connected to the inlet slit act on the rotor. It has been found that under certain conditions, these moments drastically impair the efficiency of the pump.